Recent technological advances have led to adoption of 3D scanning as standard practice in a variety of fields including medical diagnostics and inspection of manufactured parts with very high quality assurance requirements. As a result, it has become easy to generate large quantities of voxel (volume element) data, and advances in graphics software and hardware have made it possible to visualize such data. As used herein, “voxel” is not intended to be restricted to three dimensions only, but rather is defined more generally to mean a volume element in two or more dimensions.
However, things get more complicated when you attempt to do more than visualize the data. Consider, for example, the scenario wherein a bio-medical device manufacturer develops a catheter device for treating certain cardiac ailments, and they have created a design and demonstrated that it is effective on porcine test specimens. Now “all” that remains to be done is to adjust the design so that it will be effective for treating a particular human patient. The problem is to create a specific catheter design that can navigate through a particular human vascular system so it can be safely inserted from the femoral artery to the heart to provide necessary treatment.
What is needed to effectively and efficiently adjust the design for such human application is a geometric model of the relevant human anatomy that can be directly compared and used with a geometric model of the catheter. Typically, such device models are created using commercial computer-aided design (“CAD”) software.
It is at this stage where large barriers currently exist. Commercial CAD models typically consist of mathematical descriptions of a collection of patches (for example, triangular elements or nonuniform rational B-splines) that collectively define a surface of the device or object described by the model. In conventional CAD models, therefore, the catheter discussed above would consist of a set of surface patches. The data describing the relevant anatomical structure as obtained by 3D scanning (e.g., computed tomography, magnetic resonance imaging, positron emission tomography, etc.) is, however, in an entirely different form that is not compatible with conventional CAD models. Medical imaging scanners provide a 3D array of intensity values associated with each volume element. In more traditional form, the scan data can be considered as a stack of 2D images.
Conversion of the voxel-based 3D array of intensity values for use in a conventional CAD model is still a significant problem. Even restricting to a single 2D image from the stack produced by the scanner, the so-called segmentation problem (identification of a region in the image corresponding to a particular anatomical structure) has offered substantial challenges. Restricting further to the relatively easy problem of identifying hard tissue, e.g., locating the interface between bone and surrounding soft tissue, is not as simple as choosing the appropriate intensity contour in the scanned image. The boundary of the bone simply does not correspond to any iso-intensity curve, and more sophisticated methods are required. The good news is that new segmentation algorithms introduced in recent years have achieved significant progress. Colleagues in radiology have successfully combined graph cuts techniques with recent developments in level set methods to produce codes that achieve efficient segmentation of images, for example, to identify bones for orthopedic applications. From a high resolution scan, triangulated surface representations of the bones within the scanned volume can be obtained on a conventional workstation in a matter of minutes.
While improvements in solving the segmentation problem is a significant and very useful accomplishment, it does not solve all the associated problems. With 3D scan data, the common practice is to perform segmentation to generate a grid of signed distance data identifying the surface of one or more objects. An iso-surface generator is then used on the signed distance data to derive an approximate tessellation of the surface dividing interior from exterior regions of the objects. The result is either a surface mesh or, if the mesh is properly closed and appropriate topological information is provided to establish connectivity of the surface triangulation, a traditional boundary representation (“b-rep”) model. Methods for polygonizing iso-surfaces include marching cubes or dividing cubes methods, continuation methods including predictor-corrector methods, and simplicial continuation methods. In real applications, such triangulated models can contain so many triangles that typical solid modeling operations become impractical.
For example, in an ongoing project, we are using 3D printing (rapid prototyping) to fabricate models of anatomical joints from the CAD models derived using a level set algorithm. To preserve the orientation of the bones, pins are inserted into the model to connect the individual bones. However, the final operation of uniting the bone models with the pin models turns out to be troublesome. The computational load associated with constructing the union of conventional CAD models with N triangles is of order N2 (unless specialized pre-processing algorithms, such as bin sorting, are invoked), and as a result the seemingly simple operation of inserting pins to join bone models becomes impractical when the model of each bone is comprised of hundreds of thousands of triangles.
It is also desirable to employ the CAD models of segmented structures as the basis for finite element analyses. However, there are unresolved compatibility issues. The triangles on the surface of one segmented anatomical structure may not match up with the triangles modeling the surface of the adjacent structure, and such mismatches or incompatibilities strongly degrade the accuracy and efficiency of finite element analyses.
The current status is that high resolution scan data descriptions of anatomical structures can be readily obtained, but such descriptions cannot readily be employed in conventional engineering CAD systems for design/simulation tasks beyond visualization. The scan data can be translated into the CAD domain, but the translated descriptions tend to contain a large number of surfaces and are not well-suited to achieving the desired tasks. Such issues are not specific to this example problem but frequently arise in the development of typical biomedical devices and prostheses where fit and/or interference between man-made artifacts and existing anatomy are essential considerations. The biomedical industry, as well as other industries that use voxel-based data describing or imaging complex structures, would benefit from improved tools for device design and development, and society would in turn benefit from enhanced development of biomedical devices.